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2017 Peru IMO TST, 1

Find all functions $f: \mathbb{R}\rightarrow \mathbb{R}$ such that \[ f(xy-1) + f(x)f(y) = 2xy-1 \] for all x and y

2016 AMC 8, 13

Tags: selection , skrrt skrrt , love ya guys , probability

Two different numbers are randomly selected from the set ${ - 2, -1, 0, 3, 4, 5}$ and multiplied together. What is the probability that the product is $0$? $\textbf{(A) }\dfrac{1}{6}\qquad\textbf{(B) }\dfrac{1}{5}\qquad\textbf{(C) }\dfrac{1}{4}\qquad\textbf{(D) }\dfrac{1}{3}\qquad \textbf{(E) }\dfrac{1}{2}$

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